For a weak transverse gravitational wave propagating along the \(x-\) axis in
vector gravity the equivalent metric evolves as [1]}
\(g_{ik}=\eta _{ik}+\left(\begin{array}{cccc}0 & 0 & h_{0y}(t,x) & h_{0z}(t,x) \\0 & 0 & 0 & 0 \\h_{0y}(t,x) & 0 & 0 & 0 \\h_{0z}(t,x) & 0 & 0 & 0\end{array}\right) , \) 
